Just a thought.....is there anything preventing us from knitting a 'bottom-up' hat pattern in reverse order, that is to say, top-down?

Cast on the final number of stitches you would have decreased down to....and start knitting down....substituting decreases with increases?

Easy to figure the math, the number of stitches you'd need as you increase your way to the bottom, I'd think.

Absolutely no reason you can't do it that way. If the pattern depends on you doing a specific type of decrease (say ssk rather than k2tog) to make it look right, then it gets a little more complex but only as much as you have to use the "matching" type of increase to make it look the same. Most of the patterns that are within my skill set aren't that picky.

I just kicked off a hat for myself(!) yesterday where I'm sorta doing this. It's 3x3 ribbing all the way up. Or down, I guess. Requires perhaps a bit more... visualization? starting at the top, but so far it hasn't confused me too badly. I'll let you know how it goes.